In recent years, active noise reduction devices have been put in practical use. Such an active noise reduction device cancels a noise that is generated during a drive of a vehicle, such as an automobile, in a passenger compartment, and reduces the noise audible to a driver and a passenger. FIG. 19 is a block diagram of conventional active noise reduction device 901 for reducing noise N0 that is audible in space S1, such as the passenger compartment. Active noise reduction device 901 includes reference signal source 1, secondary noise source 2, error signal source 3, and signal-processing device 904.
Reference signal source 1 is an acceleration sensor installed into a chassis of a vehicle or a sensor, such as a microphone, for detecting vibration installed in space S1. Reference signal source 1 outputs a reference signal x(i) that has a correlation with noise N0. Secondary noise source 2 is a loudspeaker installed in space S1 for generating secondary noise N1. Error signal source 3 is a microphone installed in space S1 for outputting an error signal e(i) corresponding to a residual sound caused by interference between noise N0 and secondary noise N1 in space S1.
Signal-processing device 904 includes adaptive filter (ADF) 5, simulated acoustic transfer characteristic filter (hereinafter, Chat unit) 6, and least-mean-square (LMS) operation unit 7. Signal-processing device 904 operates at discrete time intervals of a sampling period Ts.
ADF 5 includes a finite impulse response (FIR) type adaptive filter composed of N filter coefficients w(k) with values updated every sampling period Ts (where k=0, 1, . . . , N−1). The filter coefficient w(k,n) at the current n-th step is updated by a filtered X-LMS (FxLMS) algorithm described in NPL 1 and NPL 2. ADF 5 determines a secondary noise signal y(n) at the current n-th step using the filter coefficient w(k,n) and the reference signal x(i) by performing a filtering operation, that is, a convolution operation expressed by formula (1).
                              y          ⁡                      (            n            )                          =                              ∑                          k              =              0                                      N              -              1                                ⁢                                    w              ⁡                              (                                  k                  ,                  n                                )                                      ·                          x              ⁡                              (                                  n                  -                  k                                )                                                                        (        1        )            
Chat unit 6 has an FIR type filter composed of a time-invariant filter coefficient C^ that simulates an acoustic transfer characteristic C(i) between an output port for outputting the secondary noise signal y(i) and an input port for acquiring the error signal e(i) of signal-processing device 904. Chat unit 6 produces a filtered reference signal r(i) obtained by performing the filtering operation, that is, the convolution operation on the filter coefficient C^ and the reference signal x(i).
LMS operation unit 7 updates the filter coefficient W(n) of ADF 5 at the current time by formula (2) using a filtered reference signal R(N), the error signal e(n), and a step-size parameter μ at the current n-th step. LMS operation unit 7 then calculates the filter coefficient W(n+1) at the next (n+1)-th step that is the next time.W(n+1)=W(n)−μ·e(n)·R(n)  (2)
The filter coefficient W(n) of ADF 5 is a vector with N rows and one column composed of N filter coefficients w(k,n) at the current n-th step, and is expressed by formula (3).W(n)=[w(0,n),w(1,n), . . . ,w(N−1,n)]T  (3)
The filtered reference signal R (n) is a vector with N rows and one column, the vector representing N filtered reference signals r(i) from the current time to the past by (N−1) steps.
Active noise reduction device 901 can determine an optimal secondary noise signal y(i) that cancels noise N0 at a position of error signal source 3 by updating the filter coefficient W(i) of ADF 5 every sampling period Ts by formula (2), thereby reducing noise N0 in space S1.
The step-size parameter μ is a parameter for adjusting a converging speed, i.e., an amount of the update of the coefficient ADF 5 at once, and is a parameter important for determining stability of adaptive operations. In order for active noise reduction device 901 to perform stable operation, it is necessary to set the step-size parameter μ to a value such that the filter coefficient W(i) does not diverge even when the reference signal x(i) has a maximum value. A condition of the step-size parameter μ that the filter coefficient W(i) converges is expressed as formula (4) described in, e.g. NPL 3.
                    0        <        μ        <                  2                      λ            MAX                                              (        4        )            
λMAX is a maximum eigenvalue of an autocorrelation matrix of the filtered reference signal R(n). In common active noise reduction device 901 using the FxLMS algorithm, a value of the step-size parameter μ is determined in consideration of a level variation of a reference signal and a noise based on formula (4). Since priority is usually given to stability, the step-size parameter μ may be often set to a smaller value to allow a certain margin.
However, when the step-size parameter μ is set smaller, an amount of the update of the filter coefficient W(i) each step becomes smaller, and it takes a time to achieve an effect of fully reducing noise N0.
Therefore, for example, PTLs 1 to 3 that determine the step-size parameter μ in accordance with a residual or an amount of convergence disclose conventional active noise reduction devices that cause the filter coefficient W(i) to converge quickly by making the step-size parameter μ variable, without fixing the step-size parameter μ.